Electron-phonon vertex correction effect in superconducting H3S
arXiv:2507.01897 · doi:10.1038/s41524-025-01818-9
Abstract
The Migdal-Eliashberg (ME) formalism provides a reliable framework for describing phonon-mediated superconductivity in the adiabatic regime, where the electronic Fermi energy exceeds the characteristic phonon energy. In this work, we go beyond this limit by incorporating first-order vertex corrections to the electron-phonon (e-ph) interaction within the Eliashberg formalism and assess their impact on the superconducting properties of H3S and Pb using first-principles calculations. For H3S, where the adiabatic assumption breaks down, we find that vertex corrections to the e-ph coupling are substantial. When combined with phonon anharmonicity and the energy dependence of the electronic density of states, the predicted critical temperature (Tc) is in very good agreement with experimental observations. In contrast, for elemental Pb, where the adiabatic approximation remains valid, vertex corrections have a negligible effect, and the calculated Tc and superconducting gap closely match the predictions of the standard ME formalism. These findings demonstrate the importance of non-adiabatic corrections in strongly coupled high-Tc hydrides and establish a robust first-principles framework for accurately predicting superconducting properties across different regimes.
17 pages, 6 figures, 13 pages of Supplementary Information
References in corpus (47)
- Optimized norm-conserving Vanderbilt pseudopotentials
- Maximally localized Wannier functions: Theory and applications
- Conventional superconductivity at 203 K at high pressures
- Wannier90 as a community code: new features and applications
- Electron-phonon interactions from first principles
- EPW: Electron-phonon coupling, transport and superconducting properties using maximally localized Wannier functions
- Crystal Structure of 200 K-Superconducting Phase of Sulfur Hydride System
- Hydrogen sulphide at high pressure: a strongly-anharmonic phonon-mediated superconductor
- Anisotropic Migdal-Eliashberg theory using Wannier functions
- Ab-initio theory of superconductivity - II: Applications to elemental metals
- What superconducts in sulfur hydrides under pressure, and why
- High temperature superconductivity in sulfur and selenium hydrides at high pressure
- High Pressure and Road to Room Temperature Superconductivity
- Origin of superconductivity and latent charge density wave in NbS
- Effect of van Hove singularities on high-Tc superconductivity in H3S
- Eliashberg Theory: a short review
- van Hove singularities and spectral smearing in high temperature superconducting H3S
- Breakdown of Migdal-Eliashberg theory; a determinant quantum Monte Carlo study
- Superconducting Phase-Diagram of H3S under High Magnetic Fields
- Theory of the special displacement method for electronic structure calculations at finite temperature
- Breakdown of the Migdal approximation at Lifshitz transitions with giant zero-point motion in H3S superconductor
- Room Temperature Superconductivity: the Roles of Theory and Materials Design
- Quantitative analysis of nonadiabatic effects in dense HS and PH superconductors
- Tuning Chemical Precompression: Theoretical Design and Crystal Chemistry of Novel Hydrides in the Quest for Warm and Light Superconductivity at Ambient Pressures
- Energy Gaps and Kohn Anomalies in Elemental Superconductors
- Anharmonic lattice dynamics via the special displacement method
- Superconductivity of Pure H3S Synthesis from Elemental Sulfur and Hydrogen
- Next-to-Leading Order Ab Initio Electron-Phonon Scattering
- Migdal's theorem and electron-phonon vertex corrections in Dirac materials
- Classifying superconductivity in compressed H3S
- Full-bandwidth Eliashberg theory of superconductivity beyond Migdal's approximation
- Notes on calculating temperature of the superconducting transition: interacting fermi gas and phonon mechanisms in non-adiabatic regime
- Ab initio theory of plasmonic superconductivity within the Eliashberg and density-functional formalisms
- Full-bandwidth anisotropic Migdal-Eliashberg theory and its application to superhydrides
- Relative importance of nonlinear electron-phonon coupling and vertex corrections in the Holstein model
- Phonon mediated superconductivity in low carrier-density systems
- EPIq : an open-source software for the calculation of electron-phonon interaction related properties
- The Wannier Function Software Ecosystem for Materials Simulations
- Archetypical "push the band critical point" mechanism for peaking of the density of states in three-dimensional crystals: Theory and case study of cubic HS
- Universal Fermi velocity in highly compressed hydride superconductors
- Coulomb interactions and conventional superconductivity: when going beyond the random phase approximation is essential
- IsoME: Streamlining High-Precision Eliashberg Calculations
- Prospect of high-temperature superconductivity in layered metal borocarbides
- Stability-superconductivity map for compressed Na-intercalated graphite
- Efficient anisotropic Migdal-Eliashberg calculations with the Intermediate Representation basis and Wannier interpolation
- Isotropic single gap superconductivity of elemental Pb: the `smiling' approach
- Nonperturbative self-consistent electron-phonon spectral functions and transport
Cited by in corpus (4)
- Gor'kov-Hedin-Baym Equations for Quantum Many-Body Systems with Spin-Dependent Interactions
- Proton Quantum Effects in HS Electronic Structure: A Multicomponent DFT study via Nuclear-Electronic Orbital Method
- Ah-SCDFT:A general approach for superconductivity with an-harmonic corrections
- Superconductivity near an Ising nematic quantum critical point in two dimensions